Finite Group Databasebeta

← C23×#10477 #19158103

Subgroups — C23×#10477 #19158103

Order 5888.

506 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C23×#461C211yesmaximal, characteristic
2C23×#1990C211yesmaximal, characteristic, complemented
3C23×#1954C211yesmaximal, characteristic
4C23×#1802C211yesmaximal, characteristic
5C2×C23×#334C211yesmaximal, characteristic, complemented
6C2×C23×#332C211yesmaximal, characteristic, complemented
7C23×#1296C211yesmaximal, characteristic, complemented
8C22×SD16×C23—21no—
9C2×C23×C4⋊Q8C2211yescharacteristic
10C2×C4×D4×C23C2211yescharacteristic
11C23×#461—22no—
12C23×#461—22no—
13C2×C23×C4⋊C8C2211yescharacteristic
14C2×C23×C4⋊C8C2211yescharacteristic
15C2×C23×C4⋊C8C2211yescharacteristic
16C2×C23×#103—21no—
17C2×C23×#102—21no—
18C2×C23×C22⋊C8—21no—
19C2×C23×C22⋊C8—21no—
20C2×C4×C8×C23C2211yescharacteristic
21C23×#384C2211yescharacteristic
22C23×#340—21no—
23C23×#340—21no—
24C23×#340—21no—
25C23×#334—22no—
26C23×#332—22no—
27C22×Q8×C23—21no—
28C22×D4×C23D411yescharacteristic
29C23×C4×C23—21no—
30C2×SD16×C23—24no—
31C2×SD16×C23—42no—
32C2×SD16×C23—42no—
33C22×C8×C23—21no—
34C22×C8×C23—21no—
35C22×C8×C23—21no—
36C22×C8×C23D411yescharacteristic
37C22×C8×C23D411yescharacteristic
38C23×C4⋊Q8—21no—
39C23×C4⋊Q8—21no—
40C23×C4⋊Q8—21no—
41C23×C4⋊Q8D412yes—
42C4×D4×C23—21no—
43C4×D4×C23—21no—
44C4×D4×C23—21no—
45C4×D4×C23—21no—
46C2×C4⋊C4×C23—21no—
47C2×C4⋊C4×C23—21no—
48C2×C4⋊C4×C23—21no—
49C2×C4⋊C4×C23—21no—
50C2×C4⋊C4×C23—21no—
51C2×C4⋊C4×C23D411yescharacteristic
52C2×C22⋊C4×C23—21no—
53C2×C42×C23C2311yescharacteristic
54C23×C4⋊C8—21no—
55C23×C4⋊C8—21no—
56C23×C4⋊C8—21no—
57C23×C4⋊C8—21no—
58C23×C4⋊C8—21no—
59C23×C4⋊C8D412yes—
60C23×#103—24no—
61C23×#102—42no—
62C23×C22⋊C8—42no—
63C23×C22⋊C8—42no—
64C4×C8×C23—21no—
65C4×C8×C23—21no—
66C24×C23—21no—
67C2×Q8×C23—22no—
68C2×Q8×C23—41no—
69C2×Q8×C23—41no—
70C2×Q8×C23—41no—
71C2×Q8×C23—41no—
72C2×Q8×C23—41no—
73C2×D4×C23—21no—
74C2×D4×C23—21no—
75C2×D4×C23—21no—
76C2×D4×C23—21no—
77C2×D4×C23—21no—
78C2×D4×C23SD1612yes—
79C22×C4×C23—21no—
80C22×C4×C23—41no—
81C22×C4×C23—41no—
82C22×C4×C23—41no—
83C22×C4×C23—41no—
84C22×C4×C23—41no—
85C22×C4×C23—41no—
86C22×C4×C23—41no—
87C22×C4×C23—41no—
88C22×C4×C23C2×D411yescharacteristic
89C22×C4×C23C2×D411yescharacteristic
90C22×C4×C23#4111yescharacteristic
91SD16×C23—48no—
92C2×C8×C23—21no—
93C2×C8×C23—21no—
94C2×C8×C23—22no—
95C2×C8×C23—21no—
96C2×C8×C23—21no—
97C2×C8×C23—21no—
98C2×C8×C23—41no—
99C2×C8×C23—41no—
100C2×C8×C23—41no—
101C2×C8×C23—41no—
102C2×C8×C23—41no—
103C2×C8×C23—41no—
104C2×C8×C23—41no—
105C2×C8×C23—41no—
106C2×C8×C23SD1612yescomplemented
107C4⋊C4×C23—21no—
108C4⋊C4×C23—22no—
109C4⋊C4×C23—22no—
110C4⋊C4×C23—21no—
111C4⋊C4×C23—41no—
112C4⋊C4×C23—41no—
113C4⋊C4×C23—41no—
114C4⋊C4×C23—41no—
115C4⋊C4×C23—41no—
116C4⋊C4×C23—41no—
117C4⋊C4×C23—81no—
118C22⋊C4×C23—41no—
119C22⋊C4×C23—41no—
120C42×C23C2×D411yescharacteristic
121C42×C23C2×D411yescharacteristic
122C42×C23#4111yescharacteristic
123C42×C23#4111yescharacteristic
124#10477C2311yesmaximal, characteristic, direct product factor, Sylow
125C23×C23—22no—
126C23×C23—41no—
127C23×C23—41no—
128C23×C23—41no—
129C23×C23—41no—
130C23×C23—41no—
131C23×C23—41no—
132C23×C23#12111yescharacteristic
133Q8×C23—42no—
134Q8×C23—42no—
135Q8×C23—81no—
136Q8×C23—81no—
137D4×C23—22no—
138D4×C23—22no—
139D4×C23—41no—
140D4×C23—41no—
141C2×C4×C23—21no—
142C2×C4×C23—21no—
143C2×C4×C23—41no—
144C2×C4×C23—42no—
145C2×C4×C23—41no—
146C2×C4×C23—41no—
147C2×C4×C23—81no—
148C2×C4×C23—81no—
149C2×C4×C23—81no—
150C2×C4×C23—81no—
151C2×C4×C23—81no—
152C2×C4×C23—81no—
153C2×C4×C23—81no—
154C2×C4×C23—81no—
155C2×C4×C23—81no—
156C2×C4×C23#12011yescharacteristic
157C2×C4×C23#12111yescharacteristic
158C2×C4×C23#12111yescharacteristic
159C2×C4×C23#12311yescharacteristic
160C2×C4×C23#12311yescharacteristic
161C2×C4×C23#12411yescharacteristic
162C2×C4×C23C2×SD1611yescharacteristic
163C2×C4×C23C2×SD1611yescharacteristic
164C2×C4×C23#13511yescharacteristic
165C2×C4×C23#13511yescharacteristic
166C2×C4×C23AGL(1,ℤ/8)11yescharacteristic
167C2×C4×C23AGL(1,ℤ/8)11yescharacteristic
168C2×C4×C23AGL(1,ℤ/8)11yescharacteristic
169C2×C4×C23#13711yescharacteristic
170C8×C23—22no—
171C8×C23—42no—
172C8×C23—41no—
173C8×C23—81no—
174C8×C23—81no—
175C2×#461C2×C2311yescharacteristic
176#1990C2×C2311yescharacteristic, complemented
177#1954C2×C2311yescharacteristic
178#1802C2×C2311yescharacteristic
179C2×#334C2×C2311yescharacteristic, complemented
180C2×#332C2×C2311yescharacteristic, complemented
181#1296C2×C2311yescharacteristic, complemented
182C22×C23—42no—
183C22×C23—42no—
184C22×C23—42no—
185C22×C23—81no—
186C22×C23—81no—
187C22×C23—81no—
188C22×C23—81no—
189C22×C23#39411yescharacteristic
190C22×C23#46111yescharacteristic
191C22×C23#46311yescharacteristic
192C22×C23#46511yescharacteristic
193C22×C23#46911yescharacteristic
194C22×C23#47111yescharacteristic
195C22×C23#47311yescharacteristic
196C4×C23—21no—
197C4×C23—21no—
198C4×C23—81no—
199C4×C23—82no—
200C4×C23—161no—
201C4×C23#44911yescharacteristic
202C4×C23#45011yescharacteristic
203C4×C23#46011yescharacteristic
204C4×C23#46411yescharacteristic
205C4×C23#46511yescharacteristic
206C4×C23#46811yescharacteristic
207C4×C23#48111yescharacteristic
208C4×C23#48211yescharacteristic
209C22×SD16—21no—
210C2×C4⋊Q8C22×C2311yescharacteristic
211C2×C4×D4C22×C2311yescharacteristic
212#461—22no—
213#461—22no—
214C2×C4⋊C8C22×C2311yescharacteristic
215C2×C4⋊C8C22×C2311yescharacteristic
216C2×C4⋊C8C22×C2311yescharacteristic
217C2×#103—21no—
218C2×#102—21no—
219C2×C22⋊C8—21no—
220C2×C22⋊C8—21no—
221C2×C4×C8C22×C2311yescharacteristic
222#384C22×C2311yescharacteristic
223#340—21no—
224#340—21no—
225#340—21no—
226#334—22no—
227#332—22no—
228C2×C23—82no—
229C2×C23#167111yescharacteristic
230C2×C23#167911yescharacteristic
231C2×C23#169311yescharacteristic
232C2×C23#170111yescharacteristic
233C2×C23#203411yescharacteristic
234C2×C23#205211yescharacteristic
235C2×C23#205511yescharacteristic
236C22×Q8—21no—
237C22×D4D4×C2311yescharacteristic
238C23×C4—21no—
239C2×SD16—24no—
240C2×SD16—42no—
241C2×SD16—42no—
242C22×C8—21no—
243C22×C8—21no—
244C22×C8—21no—
245C22×C8D4×C2311yescharacteristic
246C22×C8D4×C2311yescharacteristic
247C4⋊Q8—21no—
248C4⋊Q8—21no—
249C4⋊Q8—21no—
250C4⋊Q8D4×C2312yes—
251C4×D4—21no—
252C4×D4—21no—
253C4×D4—21no—
254C4×D4—21no—
255C2×C4⋊C4—21no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4—21no—
258C2×C4⋊C4—21no—
259C2×C4⋊C4—21no—
260C2×C4⋊C4D4×C2311yescharacteristic
261C2×C22⋊C4—21no—
262C2×C42C23×C2311yescharacteristic
263C4⋊C8—21no—
264C4⋊C8—21no—
265C4⋊C8—21no—
266C4⋊C8—21no—
267C4⋊C8—21no—
268C4⋊C8D4×C2312yes—
269#103—24no—
270#102—42no—
271C22⋊C8—42no—
272C22⋊C8—42no—
273C4×C8—21no—
274C4×C8—21no—
275C23#1047711yescharacteristic, direct product factor, Sylow
276C24—21no—
277C2×Q8—22no—
278C2×Q8—41no—
279C2×Q8—41no—
280C2×Q8—41no—
281C2×Q8—41no—
282C2×Q8—41no—
283C2×D4—21no—
284C2×D4—21no—
285C2×D4—21no—
286C2×D4—21no—
287C2×D4—21no—
288C2×D4SD16×C2312yes—
289C22×C4—21no—
290C22×C4—41no—
291C22×C4—41no—
292C22×C4—41no—
293C22×C4—41no—
294C22×C4—41no—
295C22×C4—41no—
296C22×C4—41no—
297C22×C4—41no—
298C22×C4C2×D4×C2311yescharacteristic
299C22×C4C2×D4×C2311yescharacteristic
300C22×C4#41×C2311yescharacteristic
301SD16—48no—
302C2×C8—21no—
303C2×C8—21no—
304C2×C8—22no—
305C2×C8—21no—
306C2×C8—21no—
307C2×C8—21no—
308C2×C8—41no—
309C2×C8—41no—
310C2×C8—41no—
311C2×C8—41no—
312C2×C8—41no—
313C2×C8—41no—
314C2×C8—41no—
315C2×C8—41no—
316C2×C8SD16×C2312yescomplemented
317C4⋊C4—21no—
318C4⋊C4—22no—
319C4⋊C4—22no—
320C4⋊C4—21no—
321C4⋊C4—41no—
322C4⋊C4—41no—
323C4⋊C4—41no—
324C4⋊C4—41no—
325C4⋊C4—41no—
326C4⋊C4—41no—
327C4⋊C4—81no—
328C22⋊C4—41no—
329C22⋊C4—41no—
330C42C2×D4×C2311yescharacteristic
331C42C2×D4×C2311yescharacteristic
332C42#41×C2311yescharacteristic
333C42#41×C2311yescharacteristic
334C23—22no—
335C23—41no—
336C23—41no—
337C23—41no—
338C23—41no—
339C23—41no—
340C23—41no—
341C23C23×#12111yescharacteristic
342Q8—42no—
343Q8—42no—
344Q8—81no—
345Q8—81no—
346D4—22no—
347D4—22no—
348D4—41no—
349D4—41no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—41no—
353C2×C4—42no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—81no—
357C2×C4—81no—
358C2×C4—81no—
359C2×C4—81no—
360C2×C4—81no—
361C2×C4—81no—
362C2×C4—81no—
363C2×C4—81no—
364C2×C4—81no—
365C2×C4C23×#12011yescharacteristic
366C2×C4C23×#12111yescharacteristic
367C2×C4C23×#12111yescharacteristic
368C2×C4C23×#12311yescharacteristic
369C2×C4C23×#12311yescharacteristic
370C2×C4C23×#12411yescharacteristic
371C2×C4C2×SD16×C2311yescharacteristic
372C2×C4C2×SD16×C2311yescharacteristic
373C2×C4C23×#13511yescharacteristic
374C2×C4C23×#13511yescharacteristic
375C2×C4C23×AGL(1,ℤ/8)11yescharacteristic
376C2×C4C23×AGL(1,ℤ/8)11yescharacteristic
377C2×C4C23×AGL(1,ℤ/8)11yescharacteristic
378C2×C4C23×#13711yescharacteristic
379C8—22no—
380C8—42no—
381C8—41no—
382C8—81no—
383C8—81no—
384C22—42no—
385C22—42no—
386C22—42no—
387C22—81no—
388C22—81no—
389C22—81no—
390C22—81no—
391C22C23×#39411yescharacteristic
392C22C23×#46111yescharacteristic
393C22C23×#46311yescharacteristic
394C22C23×#46511yescharacteristic
395C22C23×#46911yescharacteristic
396C22C23×#47111yescharacteristic
397C22C23×#47311yescharacteristic
398C4—21no—
399C4—21no—
400C4—82no—
401C4—81no—
402C4—161no—
403C4C23×#44911yescharacteristic
404C4C23×#45011yescharacteristic
405C4C23×#46011yescharacteristic
406C4C23×#46411yescharacteristic
407C4C23×#46511yescharacteristic
408C4C23×#46811yescharacteristic
409C4C23×#48111yescharacteristic
410C4C23×#48211yescharacteristic
411C2—82no—
412C2C23×#167111yescharacteristic
413C2C23×#167911yescharacteristic
414C2C23×#169311yescharacteristic
415C2C23×#170111yescharacteristic
416C2C23×#203411yescharacteristic
417C2C23×#205211yescharacteristic
418C2C23×#205511yescharacteristic
subgroupG/H
center, socleC23×C23#121
commutator, Frattini, cosocleC2×C42C23×C23
prime radicalC22×D4×C23D4
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C23 ◁ C2×C42×C23 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C23×#1990C2semidirect
5. C2×C23×#334C2semidirect
6. C2×C23×#332C2semidirect
7. C23×#1296C2semidirect
106. C2×C8×C23SD16semidirect
124. #10477C23direct (N × H)
176. #1990C2×C23semidirect
179. C2×#334C2×C23semidirect
180. C2×#332C2×C23semidirect
181. #1296C2×C23semidirect
275. C23#10477direct (N × H)
316. C2×C8SD16×C23semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×C23×#4612
C23×#19902
C23×#19542
C23×#18022
C2×C23×#3342
C2×C23×#3322
C23×#12962
#1047723